Question

please help with attached

Answer 1

ex 2
its division by method of detached coefficients

Answer 2

We will do this just like we would a long division question.

Write out the coefficients of the terms, if there are any missing terms put zero for the term:
\[dividend is:x^{7}-5x^{5}+7x ^{3}+2x ^{2}-6x-2\]\[divisor: x^{4}-3x ^{2}+2x+1\]
Note: the dividend is missing an x^6 and a x^4 term, the divisor is missing a x^3 term put 0 as a place holder for the missing terms. Coefficient for the dividend would be:
1 0 -5 0 7 2 -6 -2. Coefficient for the divisor: 1 0 -3 2 1

Let's divide:
1 0 -3 2 1 ) 1 0 -5 0 7 2 -6 -2
Divide the first coefficients in the dividend by the divisor (1/1=1). This gives us our first term in the answer. Note: the variables dividing is x^7/x^4 = x^3 so our first term is 1(x^3).
Multiply 1 times the coefficients in the divisor:
1 0 -3 2 1 ) 1 0 -5 0 7 2 -6 -2
1 0 -3 2 1

Add together:
1 0 -3 2 1 ) 1 0 -5 0 7 2 -6 -2
-1 0 3 -2 -1 (change the signs. put a division bar under these numbers)
0 -2 -2 6 2 (add the last 2 rows)

Second term in answer:
The first term in our sum is '0' so put '0' in our answer. The next term would be: (0)(x^2)

Third term in answer:
Divide: -2/1 (the next term is 'x'. This give us our third term in the answer (-2)(x)
Multiply 0 times the coefficients of the divisor:
1 0 -3 2 1 ) 1 0 -5 0 7 2 -6 -2
-1 0 3 -2 -1
0 -2 -2 6 2 -6
-2 0 6 -4 -2 (multiply divisor by -2, put a division bar here)

1 0 -3 2 1 ) 1 0 -5 0 7 2 -6 -2
-1 0 3 -2 -1
0 -2 -2 6 2 -6
2 0 -6 4 2 (change the signs here, put a division bar here)
-2 0 6 -4 -2 (sum of last 2 rows then bring down the -2)

Fourth term in answer:
Divide: (-2/1). The last term is a constant (-2)
1 0 -3 2 1 ) 1 0 -5 0 7 2 -6 -2
-1 0 3 -2 -1
0 -2 -2 6 2 -6
2 0 -6 4 2
-2 0 6 -4 -2
-2 0 6 -4 -2 (multiply -2 by the divisor)

1 0 -3 2 1 ) 1 0 -5 0 7 2 -6 -2
-1 0 3 -2 -1
0 -2 -2 6 2 -6
2 0 -6 4 2
-2 0 6 -4 -2
2 0 -6 4 2 (change the signs and add. Note everything cancels).

Our answer is x^3+0x^2-2x-2 = x^3-2x-2

Answer 3

Is this helpful?

Answer 4

yes it is